The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1  1  1  1  1  2  1  1 2a  1  1  1  1  1  0  1  1 2a  1  1  1  1  1  1 2a+2 2a+2  1  1  1  0  1  1  1  1  1  2  1  1  1  1  1  1  1  1  1  0  1
 0  1  1  a 3a+3  0 2a+3 a+1  a  1  0 2a+3  a  1 a+1  2 a+1 a+2 2a+3  1 a+1  a  1  0 3a a+3 2a+3 2a+1  1 2a+2 2a+1  1 a+2 3a+2 a+3 2a+1 a+3 2a+1  1  1  0 a+1 2a+1  1 3a+1 a+3  2 2a+3 2a  1 3a a+1 a+2  2 3a+2  2 2a+1 2a 2a  0 2a+3
 0  0 2a+2  0  0  0  2  2  2  2  2  2 2a+2 2a+2 2a  2 2a 2a+2 2a+2  0 2a+2 2a+2 2a 2a+2 2a  0 2a  2  2 2a+2 2a 2a+2  0  0 2a 2a 2a+2  2 2a 2a+2 2a+2  2  0  0  0  0  0 2a+2  0 2a+2 2a  2  0  2 2a  0 2a  0 2a+2  2  0
 0  0  0  2  0  2 2a+2  0  2 2a+2  2  0 2a 2a+2  0 2a+2  0  0 2a 2a  2  2 2a+2 2a+2  0 2a 2a  0 2a+2  2  2 2a  2 2a+2  0  2 2a+2  0 2a+2  2  2  2  2  2 2a  0  2  2  0 2a+2  2 2a  0 2a+2 2a  2  0  0 2a  2 2a+2
 0  0  0  0 2a+2 2a+2  2 2a+2 2a  0 2a+2  2  2 2a  2 2a 2a  2 2a+2 2a+2  0 2a+2 2a+2  2  0 2a+2  0 2a+2 2a+2 2a  2  2 2a 2a 2a+2  0  0 2a  0 2a  2 2a+2  2 2a+2 2a 2a  2  0  2  0 2a+2  0 2a+2  0 2a 2a 2a 2a+2  0  0 2a+2

generates a code of length 61 over GR(16,4) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+138x^168+180x^169+360x^171+375x^172+588x^173+780x^175+612x^176+1092x^177+1068x^179+789x^180+972x^181+1416x^183+729x^184+1452x^185+1488x^187+810x^188+1236x^189+876x^191+414x^192+540x^193+156x^195+99x^196+84x^197+39x^200+24x^204+21x^208+12x^212+18x^216+3x^220+12x^224

The gray image is a code over GF(4) with n=244, k=7 and d=168.
This code was found by Heurico 1.16 in 1.41 seconds.